Curriculum Connections
Each state in the USA and province in Canada has its own mathematics curriculum. However, the core of the North American curricula is the same despite the local differences. We suggest the connections to the Ontario Mathematics curriculum since it is our hometown province. But we emphasize the fact that the Ontario Mathematics curriculum is consistent with the Content Core Standards.
The main intended Grade band is 7-9. However, you can use the book in other Grades depending on the needs and knowledge base of your students.
Overarching Curriculum Expectations
Ancient and medieval mathematics were mostly concerned with practical applications of mathematical knowledge. The problems from old texts were about practical matters, such as areas of fields of various shapes, exchange of commodities at different rates, pricing, volumes of granaries and siege ramps of various shapes and many other real world activities. By solving these problems modern students can see mathematics as an integral and utmost necessary part of people’s lives. Thus, the following expectations are overarching expectations for almost all of the problems included in the book.
Grade 9
- make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics
Grade 7 and 8
- use knowledge of numbers and operations to solve mathematical problems encountered in everyday lifeSpecific Curriculum Expectations
Specific Curriculum Expectations
Grade 9
1.1
Make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics
Number
- research a number concept to tell a story about its development and use in a specific culture, and describe its relevance in a current context
- Problems 1.1, 1.2, 1.5, 1.18
- analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power, and use this relationship to … evaluate powers
- Problems 1.6, 1.12, 1.16
- apply an understanding of rational numbers … to solve problems
- Problems 1.3, 1.4, 1.7, 1.8, 1.9, 1.10, 1.11, 1.13, 1.14, 1.15, 1.17, 1.20
- pose and solve problems involving rates, percent, and proportions in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy
- Problems: 6.1-6.20
- apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools
- Problems: 4.1, 4.8
Algebra
- create and solve equations for various contexts, and verify their solutions
- Problems: 4.2-4.7, 4.12, 4.13, 4.17, 4.22, 4.21
Geometry and Measurement
- research a geometric concept or a measurement system to tell a story about its development and use in a specific culture or community, and describe its relevance in connection to careers and to other disciplines
- Problems: 2.1, 2.2, 2.3, 2.4, 3.8, 3.9
- solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapes
- Problems: 5.1 – 5.11
- solve problems involving different units within a measurement system and between measurement systems, including those from various cultures or communities, using various representations and technology, when appropriate
- Problems: 2.4, 2.5, 2.6, 2.7
- create and analyse designs involving geometric relationships and circle and triangle properties, using various tools
- Problems: 2.8
- solve problems involving different units within a measurement system and between measurement systems, including those from various cultures or communities
- Problems: 3.1 -3.6, 3.10 – 3.18, 6.13 – 6.16
Grade 8
1.1
Number
- use knowledge of numbers and operations to solve mathematical problems encountered in everyday life
- use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations
- Problems 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.13, 1.14, 1.15, 1.17, 1.20
- add and subtract fractions, using appropriate strategies, in various contexts
- Problems: 4.1, 4.8
- multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts
- Problems: 1.17, 4.9, 4.10, 4.14, 4.15, 4.16, 4.18, 4.19
- compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts
- Problems: 6.1- 6.20
Spatial Sense (Geometry and Measurement)
- solve problems involving the perimeter, circumference, area, volume, and surface areaof composite two-dimensional shapes and three-dimensional objects, using appropriate formulas
- Problems: 2.1-2.8, 3.1 – 3.7, 3.10 – 3.16, 3.17, 3.18
- describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle
- Problems: 5.1 – 5.11
Algebra
- create and describe patterns to illustrate relationships among rational numbers
- Problems: 1.1
- demonstrate an understanding of variables, expressions, equations, and inequalities, and apply this understanding in various contexts
- Problems: 1.19, 6.15, 6.16
- Mathematical Modelling: apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations
- Problems: 3.12, 3.15
Grade 7
1.1
Number
- use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations
- Problems 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.13, 1.14, 1.15, 1.17, 1.20
- add and subtract fractions, including by creating equivalent fractions, in various contexts
- Problems: 4.1, 4.8
- multiply and divide fractions by fractions, using tools in various contexts
- Problems: 1.17, 4.9, 4.10, 4.14, 4.15, 4.16, 4.18, 4.19
- identify proportional and non-proportional situations and apply proportional reasoning to solve problems
- Problems: 4.1, 4.8
Spatial Sense (Geometry and Measurement)
- use the relationships between the radius, diameter, and circumference of a circle to explain the formula for finding the circumference
- Problems: 2.1, 2.2, 2.3
- use the relationships between the radius, diameter, and circumference of a circle … to solve related problems
- Problems: 2.6
- show the relationships between the radius, diameter, and area of a circle, and use these relationships to explain the formula for measuring the area of a circle and to solve related problems
- Problems: 2.4, 2.5
- solve problems involving perimeter, area, and volume that require converting from one metric unitof measurement to another
- Problems: 3.1 – 3.6, 3.10, 3.11, 3.13, 3.15, 3.16
Algebra
- identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts
- Problems: 1.1
- solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions
- Problems: 6.15, 6.16